An efficient algorithm for the calculation of phase envelopes of fluid mixtures

Quiñones-Cisneros, Sergio E.; Deiters, Ulrich K.

doi:10.1016/j.fluid.2012.05.023

Cited by 20 publications

(26 citation statements)

References 16 publications

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“…needed per state point when a cubic EoS was used, approximately matches the one reported by Quiñones-Cisneros and Deiters 3 , who also observed a 10-fold larger CPU time with PC-SAFT when a Gibbs energy-based method was used. A density-based method was computationally faster when PC-SAFT was used.…”

Section: Higher-order Equations Of Statesupporting

confidence: 87%

“…Alternatively, Quiñones-Cisneros and Deiters 3 proposed to solve the multicomponent phase equilibrium problem by using a density (q) representation, where the condition for equalization of pressure is given from the expression…”

Section: Problem Formulationmentioning

confidence: 99%

“…Although it is possible to device a numerical scheme that solves Gibbs-Duhem-based differential equations for specific phase equilibrium problems, most of the methods proposed in the literature [1][2][3]19,24,25 perform a direct computation of the equilibrium for the thermodynamic conditions of interest (equilibrium point). For the multicomponent problem, usually a precalculated equilibrium point is used to get a reasonable estimate of the thermodynamic variables for the next equilibrium point and in this stepwise fashion the phase envelope is traced.…”

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confidence: 99%

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Calculation of the phase envelope of multicomponent mixtures with the bead spring method

et al. 2015

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A robust numerical scheme for the calculation of constant composition (isoplethic) phase diagrams of complex multicomponent mixtures is presented. The scheme refers to the sequential calculation of the phase envelope of a mixture by guiding the estimation for the equilibrium curve via the introduction of a "spring" that sets the slope value of the modified tangent plane distance with respect to either temperature or pressure. A simple variation of the proposed method allows direct estimation of the Cricondentherm and/or Cricondenbar points, thus avoiding the calculation of the entire phase diagram. Extensive tests of the proposed scheme for different types of phase diagrams, using both cubic and higher-order equations of state are presented. V C 2015 American Institute of Chemical Engineers AIChE J, 62: 868-879, 2016 Keywords: phase envelope, equations of state, stability analysis IntroductionAccurate and robust prediction of the phase equilibrium boundaries of multicomponent mixtures is important for the design, simulation, and optimization of various processes in oil and gas and in chemical industry. A plethora of approaches to tackle the problem have been proposed, which differ in the formulation of the problem, the numerical scheme used, and the details of the implementation. [1][2][3][4] The basis for the mathematical description of the multiphase equilibrium problem has been given by the seminal work of Gibbs who originally formulated the laws of equilibrium thermodynamics for open systems. Gibbs defined the list of variables along with the set of relations between them. These variables are the extensive and the intensive properties of each phase. Depending on the particular conditions, it is convenient to choose a different set of independent variables and use the corresponding relations to evaluate the remaining. Although there is a relative freedom to choose which variables to consider as independent, their number is strictly set by the Gibbs phase rule, according to which, the thermodynamic equilibrium state of a (nonreactive) system consisting of P phases and C components, is uniquely specified, if C2P 1 2 independent variables are set.The origin of the thermodynamic relations that govern phase equilibrium can be traced back to the first and the second law of thermodynamics for a closed system, where entropy, as an extensive and convex function of volume and energy, takes a maximum value for any given value of these variables. The vast majority of the solution schemes reformulates the problem of entropy maximization to an equivalent optimization problem of another thermodynamic potential and solves it by means of local optimization methods or nonlinear equations system solving techniques. The local properties of the thermodynamic potential in use produce the set of independent equations for the solution of the phase equilibrium problem and provide the local stability criteria.The requirement for phase stability that is location of the global minimum of the Gibbs free energy is formally addressed by the...

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Section: Higher-order Equations Of Statesupporting

confidence: 87%

Section: Problem Formulationmentioning

confidence: 99%

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confidence: 99%

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Calculation of the phase envelope of multicomponent mixtures with the bead spring method

et al. 2015

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“…In a density-based system of variables, the phase equilibrium criterion of each component having equal chemical potentials in both phases can be written as 7,8 ∇Ψ′ = ∇Ψ″ (7) where Ψ ϕ = A m ϕ ρ ϕ denotes the Helmholtz energy density of the phase ϕ and ∇ the gradient operator; the gradients have to be computed with respect to all component densities, that is, ∇ = (∂/∂ρ 1 , ∂/∂ρ 2 , ... ∂/∂ρ N ). The equal-pressure criterion then becomes…”

Section: Theorymentioning

confidence: 99%

Adiabatic Processes in the Vapor–Liquid Two-Phase Region. 2. Binary Mixtures

Imre

Quiñones-Cisneros

Deiters

2015

Ind. Eng. Chem. Res.

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The phase equilibrium conditions and entropy balance equations for multicomponent fluid mixtures are expressed with a density-based formalism ("isochoric thermodynamics"), and isentropes in the one-and two-phase region are computed from equations of state; here the Peng−Robinson equation is used as an example. Griffiths' theoremone-and two-phase isentropes meet at a maxcondenbar point (pressure maximum of an isopleth) with equal slopescould be confirmed. For chemically similar compounds at subcritical conditions, the resulting isentrope patterns are similar to those of pure fluids. If one of the components is supercritical, it is possible that, along a part of a two-phase isentrope, the liquid phase has a higher molar entropy than the vapor phase ("entropic inversion"). The phenomenon not only poses a numerical problem, but is also relevant for the question whether a two-phase isentrope can run into the llg three-phase curve.

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“…There are existing efforts in the literature to tackle some of the reliability issues with phase envelope construction by constructing lines of constant composition (isopleths) cutting through the phase envelope, but there is comparatively less literature on the construction of lines of constant temperature or pressure around phase envelopes.…”

Section: Introductionmentioning

confidence: 99%

On the construction of binary mixture p‐x and T‐x diagrams from isochoric thermodynamics

Bell

Deiters

2018

AIChE Journal

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In this work, we describe how to efficiently and reliably calculate p‐x and T‐x diagrams for binary mixtures of fluids. The method is based on the use of the Helmholtz energy density as the fundamental thermodynamic potential. Through the use of temperature and molar concentrations of the components as the independent variables, differential relationships can be constructed along the phase envelope surface, and this system of differential equations is then integrated to construct isotherms and isobars cutting through the phase envelope. The use of the Helmholtz energy density as the fundamental potential allows several models to be considered in this formalism, including cubic equations of state (Peng‐Robinson, GC‐VTPR, etc.) as well as high‐accuracy multifluid equations of state (the so‐called GERG mixture model). Examples of each class are presented, demonstrating the flexibility of this method. Source code, examples, and comprehensive analytic derivatives are provided in the Supporting Information. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2745–2757, 2018

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An efficient algorithm for the calculation of phase envelopes of fluid mixtures

Cited by 20 publications

References 16 publications

Calculation of the phase envelope of multicomponent mixtures with the bead spring method

Calculation of the phase envelope of multicomponent mixtures with the bead spring method

Adiabatic Processes in the Vapor–Liquid Two-Phase Region. 2. Binary Mixtures

On the construction of binary mixture p‐x and T‐x diagrams from isochoric thermodynamics

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